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Abstract The angular moments of the Z boson can be used as analyzers for the underlying production dynamics for the $$t{{\bar{t}}} Z$$ t t ¯ Z and tZj processes. In this manuscript, we derive these angular moments at leading and next-to-leading order in QCD at the LHC. We show that these observables work as efficient probes to beyond the Standard Model effects, considering the Standard Model Effective Field theory framework. Remarkably, we observe that these probes unveil blind directions to CP-odd operators, providing sizable new physics sensitivity at the 14 TeV LHC with 3 ab $$^{-1}$$ - 1 of data.